The art of pulling the goalie is one that takes a fair amount of awareness with how the game is going. In most games, a goalie would be called to the bench whenever a penalty is pending against the opposing team. In rare instances, you might find a coach elect to yank the netminder with an offensive zone draw late in any given period. This is extremely rare however, and shouldn’t be thought of as a regular occurrence.
One of the great spectacles in sports however is when your team is playing with a deficit on the scoreboard, and late in the 3rd period elect to pull the goalie and replace him with an extra attacking skater on the ice in the hopes it will lead to a game-tying goal.